Time delay estimation

ABSTRACT

A time differential is estimated between a plurality of signals by determining a filter response of a first electrical signal with a first filter array, determining a filter response of a second electrical signal with a second filter array, and determining, based at least on the filter response of the first electrical signal and the filter response of the second electrical signal, a time differential between the first electrical signal and the second electrical signal. A first optical signal is converted into the first electrical signal and a second optical signal is converted into the second electrical signal. The filter response of the first electrical signal and the filter response of the second electrical signal are sampled and the time differential between the first electrical signal and the second electrical signal is determined based at least on the sampled filter response of the first electrical signal and the sampled filter response of the second electrical signal.

This application claims the benefit of U.S. Provisional Application No.60/994,639 filed Sep. 20, 2007 which is incorporated herein byreference.

BACKGROUND OF THE INVENTION

The present invention relates generally to time delay estimation andmore particularly to circuits for time delay estimation in laserscanning.

Increasing complex systems require increasingly accurate andfine-grained time delay estimation. For example, some laser scanningsystems measure a time delay between a sent and received laser pulse todetermine the distance to an object. The time delay between the sendingof the pulse and the receiving of the reflected pulse is very small andmust be measured with great accuracy—on the order of less than 10nanoseconds—in order to properly determine the desired distancemeasurement. Conventional methods of time delay estimation are eitherprohibitively expensive or unable to accurately detect such small timeintervals.

In a laser scanning system, the distance to a remote object is measuredby reflecting some energy of a short laser pulse off the object. Whenthe pulse is emitted, some of its energy is diverted immediately and issent to an avalanche photo diode. The difference in time between thetime the pulse is emitted and the time the reflected pulse is receivedat the emitter, multiplied by the speed of light, provides an estimateof the distance to the remote object. In order for the distancemeasurement to have accuracy on the order of about a millimeter, thetime estimate must be accurate to within a few picoseconds.

Conventional techniques of time delay estimation in laser scanning aredescribed in U.S. Pat. No. 6,665,055, entitled “Light-Wave RangefinderUsing a Pulse Method” (Ohishi), U.S. Pat. No. 5,619,317, entitled“Light-Wave Distance Meter Based on Light Pulses” (Oishi), and U.S.Patent Application No. 2005/0052952, entitled “Time Interval MeasurementDevice” (Panek).

Ohishi and Oishi disclose techniques for introducing an electrical pulseinto a tuned filter. This has the effect of stretching the pulse into aseries of damped oscillations. To further reduce the analog measurementbandwidth, this waveform is periodically sampled at a low frequency witha small increase of time delay between each sample. However, asdiscussed above, these methods fail to provide sufficient accuracy forshort time interval estimation and thus cannot provide a qualitydistance measurement.

Panek utilizes improvements in the speed and cost of high speed samplersto use a slightly different approach. Panek discloses sampling in realtime when the bandwidth of the tuned filter is narrower than half thesampling bandwidth. However, only a small part of the pulse energy isused in such an approach. Only a small dynamic range of pulse durationscan be measured because, as longer pulses are introduced, the filterresponse is necessarily diminished. This approach also compromisessystem accuracy by separately introducing a calibration pulse into eachchannel.

Related methods of time delay estimation used a Nutt interpolator.However, the Nutt interpolator cannot measure pulse widths wider thanthe resolution of the filter used and information is lost. Accordingly,such a method cannot properly account for the increased resolutionaccuracy required in modern time delay estimation.

Accordingly, improved systems and methods of time delay estimation arerequired.

BRIEF SUMMARY OF THE INVENTION

The present invention generally provides methods of time delayestimation. In one embodiment, estimating a time differential between aplurality of signals includes determining a filter response of a firstelectrical signal with a first filter array, determining a filterresponse of a second electrical signal with a second filter array, anddetermining, based at least on the filter response of the firstelectrical signal and the filter response of the second electricalsignal, a time differential between the first electrical signal and thesecond electrical signal. In a light detection and ranging (LIDAR)application, for example, a first optical signal is converted into thefirst electrical signal and a second optical signal is converted intothe second electrical signal. The filter response of the firstelectrical signal and the filter response of the second electricalsignal are sampled and the time differential between the firstelectrical signal and the second electrical signal is determined basedat least on the sampled filter response of the first electrical signaland the sampled filter response of the second electrical signal.

In some embodiments, the second electrical signal is amplified and afilter response of the amplified second electrical signal is determinedwith a third filter array. Either the filter response of the secondelectrical signal or the filter response of the amplified secondelectrical signal is then selected as the second electrical signal fordetermining the time differential.

In another embodiment, a method for calibrating the time delayestimation circuit includes generating a calibration pulse, determininga filter response of the calibration pulse with a first filter array,determining a filter response of the calibration pulse with a secondfilter array, and determining, based at least on the filter response ofthe calibration pulse determined with the first filter array and thefilter response of the calibration pulse determined with the secondfilter array, a phase correction. In some embodiments, the filterresponse of the calibration pulse determined with the first filter arrayand the filter response of the calibration pulse determined with thesecond filter array are sampled. The phase correction is determinedbased at least on the sampled filter response of the calibration pulsedetermined with the first filter array and the sampled filter responseof the calibration pulse determined with the second filter array.

These and other advantages of the invention will be apparent to those ofordinary skill in the art by reference to the following detaileddescription and the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram of a time delay estimation circuit according to anembodiment of the invention;

FIG. 2 depicts a flowchart of a method of time delay estimationaccording to an embodiment of the present invention;

FIG. 3 depicts a graph of exemplary filter frequencies aliased to thebase band;

FIG. 4 depicts a graph of exemplary filter responses;

FIG. 5 depicts a graph on an exemplary filter response as a function ofpulse width; and

FIG. 6 shows a flowchart of a method of calibration of a time delayestimation circuit according to an embodiment of the present invention.

DETAILED DESCRIPTION

At least one embodiment of the present invention provides techniques formeasuring the time between two optical pulses (e.g., a start pulse and astop pulse) that relate to the transit time between a measurementinstrument and a distant object. Of course, this may be extended tomeasure or estimate the time between any two events using the inventivetechniques described herein. When applied to laser scanning, opticalpulses are converted into an electrical signal to enable an electronicdevice to make an estimate of the time differential.

FIG. 1 depicts a time delay estimation circuit 100 according to anembodiment of the present invention. Though described herein as ageneral circuit with specific reference to components of that circuit,one of skill in the art will recognize that the functions of time delayestimation circuit may be performed by any appropriate combination ofelectrical and/or electromechanical devices.

Circuit 100 includes sensor 102, which receives one or more inputs.Sensor 102 passes signals indicative of the inputs to switch 104. Insome embodiments, switch 104 selectively passes at least a portion ofthe signals to start pulse switch 106, which allows signals to pass tostart pulse filter array 108. In alternative embodiments, switch 104allows signals to pass directly to start pulse filter array 108.Substantially simultaneously, sensor 102 passes signals to comparator110.

In some embodiments, switch 104 also selectively passes at least aportion of the signals to low gain switch 112 and high gain switch 114.In turn, low gain switch 112 passes the signals to low gain filter array116 and high gain switch 114 passes the signals through amplifier 118 tohigh gain filter array 120. In alternative embodiments, switch 104allows signals to pass directly to low gain filter array 116 and throughamplifier 118 to high gain filter array 120.

Gain selection switch 122 selectively allows signals propagating throughlow gain filter array 116 and/or high gain filter array 120 to pass tosampler 124 to be sampled before passing to processor 128. Similarly,signals propagating through start filter array 108 pass to sampler 126to be sampled before passing to processor 128. Processor 128, Inaddition to receiving signals from samplers 124 and 126 may also be incommunication with and/or control switches 104, 106, 112, 114, and 120as will be discussed further below with respect to FIG. 2.

In some embodiments, circuit 100 also includes a calibration pulsegenerator 130. Calibration pulse generator 130 is configured to transmitsignals (e.g., electrical signals, pulses, etc.) to start switch 106,low gain switch 108, and high gain switch 114.

Sensor 102 may be any appropriate sensor, such as a photodetector. In atleast one embodiment, sensor 102 is an avalanche photodiode. In analternative embodiment, sensor 102 is an amplified avalanche photodiode.In some embodiments, sensor 102 is configured to convert an incominginput signal (e.g., an optical pulse, a pulse pair, etc.) into anelectrical signal. Sensor 102 may receive a pulse pair (e.g., a startpulse and a stop pulse) and convert the optical signals into electricalsignals.

Switches 104, 106, 112, 114, and 122 may be any appropriate switchcapable of receiving and/or selectively passing signals (e.g.,electrical signals indicative of optical pulses). In some embodiments,switches 104, 106, 112, 114, and 122 may be analog or bilateralswitches. In at least one embodiment, switch 104 is an RF analog switch.Switches 106, 112, and 114 may be capable of switching between incomingsignals from sensor 102 via switch 104 and calibration pulse generator130. Switch 122 may directed by processor 128 to utilize the signal fromeither filter array 116 or filter array 120 that is most likely to be inan appropriate range of amplitude.

Filter arrays 108, 116, and 120 may be any appropriate combinations(e.g., banks, stacks, etc.) of filters (e.g., electronic filters,electromechanical filters, etc.) such as surface acoustic wave (SAW)filters, comb filters, band pass filters, or the like. In at least oneembodiment, filter arrays 108, 116, 120 are SAW filters centered atapproximately 140 MHz and approximately 80 MHz and have a band width ofapproximately 8 MHz. That is, each filter array 108, 116, 120 may havemultiple filters (e.g., one filter centered at approximately 140 MHz andone filter centered at approximately 80 MHz) and signals may be furthersplit to pass through all the filters in parallel in the filter arrays.The output of the filters is recombined before passing further throughtime delay estimation circuit 100. Other types of filters, centers, andband widths may be used as appropriate.

Comparator 110 may be any appropriate device or devices, such as ananalog comparator, for comparing multiple signals. Comparator 110 may beconfigured to detect a start pulse (e.g., from sensor 102), a stop pulse(e.g., from low gain switch 112), and an amplified stop pulse (e.g.,from amplifier 118) and send signals indicative of these pulses toprocessor 128. Comparator 110 may thus use counters operating at apredetermined frequency. In at least one embodiment, the counters arerunning at 250 MHz.

Samplers 124 and 126 may be any appropriate sampling devices. In atleast one embodiment, samplers 124 and 126 are and/or include high speedanalog to digital converters. Samplers 124 and 126 may thus beconfigured to determine rising and falling edges of the start pulse, thestop pulse, and the amplified stop pulse as well as any calibrationpulses.

Processor 128 may be any appropriate computer, processor, or combinationof components configured to, among other things, collect data associatedwith time measurement and/or estimation, estimate differential timemeasurements, communicate with other processors (not shown), and controlthe states of switches 104, 106, 112, 114, and 122.

Processor 128 may control the overall operation of circuit 100 byexecuting computer program instructions which define such operation. Thecomputer program instructions may be stored in a storage device (notshown) (e.g., magnetic disk, database, etc.) and loaded into memory (notshown) when execution of the computer program instructions is desired.Thus, applications for performing the herein-described method steps inmethods 200 and 300 are defined by the computer program instructionsstored in the memory and/or storage and controlled by the processor 128executing the computer program instructions. The processor 128 may alsoinclude one or more network interfaces (not shown) for communicatingwith other devices via a network. Processor 128 may include one or morecentral processing units, read only memory (ROM) devices and/or randomaccess memory (RAM) devices. One skilled in the art will recognize thatan implementation of an actual controller could contain other componentsas well, and that the processor of FIG. 1 is a high level representationof some of the components of such a controller for illustrativepurposes.

According to some embodiments of the present invention, instructions ofa program (e.g., controller software) may be read into memory, such asfrom a ROM device to a RAM device or from a LAN adapter to a RAM device.Execution of sequences of the instructions in the program may cause theprocessor 128 to perform one or more of the method steps describedherein, such as those described above with respect to methods 200 and300. In alternative embodiments, hard-wired circuitry or integratedcircuits may be used in place of, or in combination with, softwareinstructions for implementation of the processes of the presentinvention. Thus, embodiments of the present invention are not limited toany specific combination of hardware, firmware, and/or software. Thememory may store the software for the processor 128, which may beadapted to execute the software program and thereby operate inaccordance with the present invention and particularly in accordancewith the methods described in detail above. However, it would beunderstood by one of ordinary skill in the art that the invention asdescribed herein could be implemented in many different ways using awide range of programming techniques as well as general purpose hardwaresub-systems or dedicated controllers.

Such programs may be stored in a compressed, uncompiled and/or encryptedformat. The programs furthermore may include program elements that maybe generally useful, such as an operating system, a database managementsystem, and device drivers for allowing the controller to interface withcomputer peripheral devices, and other equipment/components. Appropriategeneral purpose program elements are known to those skilled in the art,and need not be described in detail herein.

Calibration pulse generator 130 may be any appropriate component orgroup of components able to transmit substantially simultaneous signalsto start pulse switch 106, low gain switch 108, and high gain switch114. Further discussion of calibration in relation to calibration pulsegenerator is included below with respect to FIG. 6.

FIG. 2 depicts a flowchart of a method 200 of time delay estimationaccording to an embodiment of the present invention. Time delayestimation circuit 100 or a similar time delay estimator may be used toperform the various steps of method 200. The method starts at step 202.

In step 204, a first signal is received at sensor 102. The signal may bean optical signal, such as a start pulse or signal from a laser scanningapparatus. In step 206, the first signal is converted into an electricalsignal.

In step 208, a course estimate is made of the time of arrival of thefirst signal. The course estimate may be made by comparator 110 inconjunction with counters in processor 128. In some embodiments, such anestimate may be accurate to within a few nanoseconds.

In step 210, a filter response of the first signal is determined. Thefilter response may be determined by the start filter array 108. Asdiscussed above, in some embodiments, two sets of filters are used infilter array 108. For example, one set of filters may be 80 MHz and onset of filters may be 140 MHz. The first signal is split and half of thesignal enters one set of filters (e.g., the 80 MHz filters) and theother half of the signal enters the other set of filters (e.g., the 140MHz filters). The output (e.g., filter response) is recombined beforepassing to step 212.

In practice, the pass bands should not overlap when aliased down to thebase band. In the exemplary embodiment described herein, with samplingat 125 MHz, the 140 MHz frequencies are aliased to 15 MHz and the 80 MHzfrequencies are aliased to 45 MHz. FIG. 3 depicts a graph 300 ofexemplary filter frequencies aliased to the base band with a 125 MHzsampling rate resulting in a pulse amplitude 302 from one filter (e.g.,the 80 MHz filter) and a pulse amplitude 304 from the other filter(e.g., the 140 MHz filter).

FIG. 3 shows “aliased” filter responses. The center of the X axis of thegraph is at zero frequency. There are positive and negative frequenciesshown in the graph. The response designated as pulse amplitude 304 isthe positive frequency alias of the 140 MHz filter response. Thecorresponding 140 MHz negative frequency alias is the mirror-imageresponse immediately to the left of pulse amplitude 304. The responsedesignated as pulse amplitude 302 is the negative-frequency alias of the80 MHz response. The corresponding 80 MHz positive-frequency alias isthe response to the right of the alias designated as pulse amplitude304. Note that sampling is equivalent to radio frequency “mixing” (e.g.,a multiplication process), just viewed from a different perspective. So,one of ordinary skill in the art would recognize not only thepositive-frequency aliases but also the negative frequency aliases, aswell as the frequency-order inversion that happens for the aliasedresponses from the 140 MHz filter (since the sample frequency is lessthan the filter frequency).

FIG. 4 depicts a graph 400 of exemplary filter responses with a 125 MHzsampling rate. Unaliased filter responses 402 and 404 are centeredaround the respective filter frequencies of 80 MHz and 140 MHz, asdiscussed above. The 80 MHz and 140 MHz frequencies are aliased down toresponses 406 (e.g., at 45 MHz) and 408 (e.g., at 15 MHz), respectively.

Use of multiple filters allows a broader range of pulse widths to beproperly addressed. The spectrum of a clipped Gaussian pulse hassin(x)/x envelope response nulls; the frequency location of the nullwill vary as a function of pulse width. When the pulse width is close tothe reciprocal of the center frequency, the responses from the risingand falling edges approximately cancel each other out and there is verylittle signal. In the exemplary embodiment discussed herein, the 140 MHzfilters have the largest response to a pulse approximately three to fournanoseconds wide and the smallest response to a pulse approximatelyseven seconds wide. The 80 MHz filters have the largest response to apulse approximately seven nanoseconds wide and the smallest response toa pulse approximately twelve to thirteen seconds wide. Using bothfilters ensures there will be a significant response for pulses up tothirteen nanoseconds wide. Additionally, more of the energy of theoriginal pulse may be used. For pulse widths in which both filtersprovide a good response, twice as many frequencies are used in the timedelay estimation, which improves the accuracy of the measurement. FIG. 5depicts a graph 500 on an exemplary filter response as a function ofpulse width. Pulse 502 represents the signal through a first filter(e.g., the 80 MHz filter) and pulse 504 represents the signal through asecond filter (e.g., the 140 MHz filter).

After the filter response is determined as described above in step 210,the filter response is sampled by sampler 126 in step 212. That is,sampler 126 samples the filter response determined in step 210. In atleast one embodiment, the filter response is sampled at a high rate(e.g., approximately 125 MHz). Of course, other sampling rates may beutilized.

It is necessary that the sample-and-hold part of an analog-to-digitalconverter (ADC) have enough bandwidth to allow the original frequencycontent to pass correctly into the rest of the ADC. So, for example, ifthe 125 MHz ADC has a sample-and-hold input bandwidth of 60 MHz, none ofthe energy from the SAW filters (e.g., filter arrays 108, 116, 120) willbe available for the ADC to process.

In step 214, a second signal is received at sensor 102. The secondsignal may be an optical signal, such as a stop or return pulse orsignal at a laser scanning apparatus. In step 216, the second signal isconverted into an electrical signal.

In step 218, a course estimate is made of the time of arrival of thesecond signal. The course estimate may be made by comparator 110 inconjunction with counters in processor 128. In some embodiments, such anestimate may be accurate to within a few nanoseconds.

In step 220, the second signal is split into two channels. That is, thesecond signal is split, sampled, copied, or otherwise augmented toprovide a signal to both high gain switch 114 and low gain switch 112.In this way, one portion of the signal (e.g., one channel) is providedalong an amplified path (e.g., through high gain switch 114, amplifier118 and high gain filter array 120) and another portion of the signal(e.g., another channel is provided along an unamplified path (e.g.,through low gain switch 112 and low gain filter array 116). The use oftwo channels in this manner allows accurate measurement of a much widerdynamic range of second signals (e.g., stop/return pulses, etc.). Thepropagation of the second signal portions through the filter arrays 116and 120 takes a relatively long amount of time, so the processor 128 maydirect switch 122 to only pass the signal from the filter arrayprocessing a signal likely to be in an appropriate amplitude range.

In step 222, a filter response of the low gain portion of the secondsignal is determined. That is, a filter response is determined for theportion of the signal passing through the low gain filter array 116after being split in step 220. The filter response may be determined bythe low gain filter array 116. As discussed above, in some embodiments,two sets of filters are used in filter array 116. For example, one setof filters may be 80 MHz and on set of filters may be 140 MHz. Theportion of the second signal is split and half of the signal enters oneset of filters (e.g., the 80 MHz filters) and the other half of thesignal enters the other set of filters (e.g., the 140 MHz filters). Theoutput (e.g., filter response) is recombined before passing to step 228.

In step 224, the high gain portion of the second signal is amplified byamplifier 118. That is, the channel passing through the amplified pathis amplified by amplifier 118 before passing to step 226 to be filtered.

In step 226, a filter response of the amplified portion of the secondsignal is determined. The filter response may be determined by the highgain filter array 120. As discussed above, in some embodiments, two setsof filters are used in filter array 120. For example, one set of filtersmay be 80 MHz and on set of filters may be 140 MHz. The portion of thesecond signal is split and half of the signal enters one set of filters(e.g., the 80 MHz filters) and the other half of the signal enters theother set of filters (e.g., the 140 MHz filters). The output (e.g.,filter response) is recombined before passing to step 228.

In at least one embodiment method step 222 is performed in parallel withmethod steps 224 and 226. That is, a portion of the second signal passesthrough the unamplified path and is filtered by filter array 116 atsubstantially the same time as another portion of the second signalpasses through the amplified path and is amplified by amplifier 118 andis filtered by filter array 120.

In step 228, a filter response is selected. In at least one embodiment,processor 128 directs switch 122 to allow a filter response from eitherthe amplified path or the unamplified path to pass to sampler 124. Asdiscussed above, processor 128 may direct switch 122 to only pass thesignal from the filter array processing a signal likely to be in anappropriate amplitude range.

The appropriate filter response is passed to sampler 124 and the filterresponse is sampled in step 230. That is, sampler 124 samples the filterresponse selected in step 228. In at least one embodiment, the filterresponse is sampled at a high rate (e.g., approximately 125 MHz). Ofcourse, other sampling rates may be utilized.

In step 232, a time delay is estimated. That is, a time differentialbetween the first electrical signal and the second electrical signal isdetermined based at least on the filter response of the first electricalsignal and the filter response of the second electrical signal.

To estimate the time delay between two signals (e.g., the first andsecond electrical signals, two optical signals, etc.), Fouriertransforms F_(s) and G_(s) of the sampled filter responses determined insteps 212 and 230, respectively, are found. At each frequency s in apass band, magnitude M_(s)=|F_(s)∥G_(s)| and the phase differenceP_(s)=(arg(F_(s)/G_(s))+K_(s))/2π, which may be predetermined and/oradjusted by a value given by a calibration pulse, discussed below withrespect to FIG. 6, are computed.

For the Fourier transforms described above, let F(s) be a Fouriertransform of a given signal f(t). Using the time shifting property ofFourier transforms, the transform of f(t−t₀) is F(s)e^(2πit) ⁰ ^(s). Inother words, the transform off is shifted by a phase and the phase shiftat frequency s is t₀s. Given two signals f(t) and g(t) that are expectedto differ by a time shift, the best estimate for the shift is the valuet₀ that maximizes ∫_(−∞) ^(∞)f(t−t₀)g(t)dt=∫_(−∞) ^(∞f(t−t) ₀)g(t)dt=∫_(−∞) ^(∞)F(s) G(s)e^(2πit) ⁰ ^(s)ds. This utilizes Parseval'srelation and the fact that g is real valued.

In the case of a discrete Fourier transform of a band-limited signalsampled at frequency w₀, an analogous relation of

${\sum\limits_{k}{{f\left( t_{k} \right)}{g\left( t_{k + d} \right)}}} = {\sum\limits_{s}{{F(s)}{\overset{\_}{G}(s)}{\mathbb{e}}^{2\;\pi\;{\mathbb{i}}\;{{ds}/w_{0}}}}}$exists.

$\sum\limits_{k}{{f\left( t_{k} \right)}{g\left( t_{k + d} \right)}}$is the sample correlation defined only when d is an integer, but

$\sum\limits_{s}{{F(s)}{\overset{\_}{G}(s)}{\mathbb{e}}^{2\;\pi\;{\mathbb{i}}\;{{ds}/w_{0}}}}$is a continuous function defined for all real values of d. When d is notintegral, this may be interpreted as the sample correlation that wouldbe obtained by reconstructing the band-limited continuous signal fromits constituent frequencies, shifting by d units in the time domain,resampling at the integer points, and computing the sample correlation.

This expression is maximized for a fixed frequency s when st₀ is equalto the measured phase difference between F(s) and G(s). To find theglobal optimum, F(s)=|F(s)|e^(2πθ) ⁰ ^((s)) and G(s)=|G(s)|e^(2πθ) ¹^((s)) may be expressed in terms of their magnitudes and phases as

${\sum\limits_{s}{{F(s)}{\overset{\_}{G}(s)}{\mathbb{e}}^{2\;{\pi\mathbb{i}}\; t_{0}s}}} = {\sum\limits_{s}{{{F(s)}}{{G(s)}}{{\mathbb{e}}^{2\;{\pi{({{\theta_{0}{(s)}} - {\theta_{1}{(s)}} + {t_{0}s}})}}}.}}}$Thus, the real part is Σ|F(s)∥G(s)|cos(2π(θ₀(s)−θ₁(s)+t₀s)). To thelowest order term, maximizing this quantity is the same as minimizing

$\sum\limits_{s}{{{F(s)}}{{G(s)}}{\left( {{\theta_{0}(s)} - {\theta_{1}(s)} - {t_{0}s}} \right)^{2}.}}$This may be achieved when

$t_{0} = {\frac{\sum\limits_{s}{{{F(s)}}{{G(s)}}\left( {{\theta_{0}(s)} - {\theta_{1}(s)}} \right)s}}{\sum\limits_{s}{{{F(s)}}{{G(s)}}s^{2}}}.}$

At a single frequency s, signals that are off by a full period cannot bedistinguished so P_(s) is defined only with respect to the integers.Referring to the completed sampled filtered signal is insufficient toresolve this ambiguity. The signal looks like a modulated sinusoid atthe center frequency of the filter. Because it is coarsely sampled, inthe presence of noise it is difficult to distinguish between a signaland the same or a similar signal that is shifted by any number ofperiods. Accordingly, the phase must be unwound. That is, the properphase must be resolved by some means. In some embodiments, the phase isunwound by using coarse counters described above. In alternativeembodiments, the phase is unwound by combining information fromdifferent frequencies.

In embodiments in which the phase is unwound with counters, at eachpulse the counters are triggered when the pulse rises above a certainthreshold. The counters are again triggered when the pulse falls belowthe threshold. Averaging these two counter values provides an estimateof the location of the pulse center. In some embodiments, this estimatemay be accurate to less than the frequency period of the counters, e.g.four nanoseconds for a 250 MHz clock.

Let s_(c) be a particular frequency near the center of the pass band inMHz. For each pulse, let F_(s) _(c) be the value of the fast Fouriertransform as s_(c). Let C_(p) be the counter value estimate of the pulsecenter and C_(f) be the counter value corresponding to the start of thedata used in the FFT. Let Φ_(s) _(c) be the fraction part of arg(F_(s)_(c) )/2π+(C_(f)−C_(p))·s_(c)/counterfrequency. Φ_(s) _(c) provides anestimate of the phase of the filtered pulse at s_(c) measured relativeto C_(p), the counter value when the pulse arrived. By comparing thevalue of Φ_(s) _(c) for a particular pulse to the average value of Φ_(s)_(c) over many pulses, Φ_(s) _(c) ^(av), the arrival of the pulse in thecounter cycle may be estimated. The average Φ_(s) _(c) ^(av) does nothave significant drift with time or temperature and may thus be known inadvance. In situations in which the average is not known, it may becomputed dynamically by generating a number (e.g., approximately a fewhundred) of pulses and keeping a basic histogram of the phases Φ_(s)_(c) in the circle. In this way, an estimate of the arrival of the pulsein the clock cycle may be obtained. To be precise, the raw countervalues may be adjusted by (Φ_(s) _(c) −Φ_(s) _(c) ^(av))/s_(c). A courseestimate of the time delay may be achieved by making such an estimatefor each pulse. The phase P_(s) may then be adjusted at each frequencyby an integer N_(s) to obtain a phase estimate of Φ_(s)=P_(s)+N_(s),which corresponds to the coarse estimate.

In embodiments in which counters are not available, the phase may beunwound by estimating a slope. For each frequency s in the pass band, aphase estimate P_(s) gives a time delay estimate of t_(s)=P_(s)/s.Adjusting P_(s) by an integer N gives a new estimate t_(s)′=(P_(s)+N)/s.To choose the optimal value of N, the parameters τ and n that give theoptimal least squares estimate for the set of equations τs=P_(s)+n foreach s in the pass band is found. Then, N is set to the closest integerto n and this is used to compute all of the absolute phasesΦ_(s)=P_(s)+N_(s) before making the final time delay estimate.

Once each phase P_(s) has been adjusted by an integer using one of theherein described methods or another appropriate method to determine theabsolute phase difference Φ_(s), the values from the differentfrequencies are average to find the optimal time delay estimate

$T = {\frac{\sum\limits_{s}{M_{s}\Phi_{s}s}}{\sum\limits_{s}{M_{s}s^{2}}}.}$

The method ends at step 234.

FIG. 6 shows a flowchart of a method 600 of calibration of a time delayestimation circuit according to an embodiment of the present invention.Method 600 may be performed by various components of time delayestimation circuit 100, described above with respect to FIG. 1.Generally, a calibration pulse may be used to account for differencesbetween filter arrays (e.g., filter arrays 108, 116, 120). The phaseresponse of filters such as SAW filters is sensitive to temperature.Without calibration, phase responses would present as error in a timedelay estimate due to temperature drift, manufacturing discrepancies,and/or other factors. The method starts at step 602.

In step 604, a pulse is generated by calibration pulse generator 130.The calibration pulse is a single pulse that is split and sent to filterarrays 108, 116, and 120 via start switch 106, low gain switch 112, andhigh gain switch 114, respectively.

In step 606, a filter response for each filter array is determined. Thismay be similar to the filter responses determined above in steps 210,222, and 226 of method 200.

In step 608, the filter responses for each filter array 108, 116, 120are sampled. This may be similar to the sampling described above withrespect to method steps 212 and 230 of method 200.

In step 610, a phase correction for each frequency in the pass band isdetermined. In this way, a stable zero-time reference is determined. Inat least one embodiment, a fast Fourier transform (FFT) is applied toeach sampled pulse from step 608. This provides a collection of complexnumbers representing the phase and amplitude at each frequency. For eachfrequency s in the pass band, complex numbers F_(s) and G_(s) are givenby the FFT for the start channel (e.g., for the calibration pulsetraveling through filter array 108) and for the return channel (e.g.,for the calibration pulse traveling through filter arrays 116 and 120),respectively, at each frequency. The correction factor K_(s) to beapplied at frequency s is given by the phase difference asK_(s)=arg(G_(s)/F_(s)). In this way, the phase correction is determined.The phase correction may be used as described above with respect tounwinding the phase for time delay estimation in step 232 of method 200.

The method ends at step 612.

The foregoing Detailed Description is to be understood as being in everyrespect illustrative and exemplary, but not restrictive, and the scopeof the invention disclosed herein is not to be determined from theDetailed Description, but rather from the claims as interpretedaccording to the full breadth permitted by the patent laws. It is to beunderstood that the embodiments shown and described herein are onlyillustrative of the principles of the present invention and that variousmodifications may be implemented by those skilled in the art withoutdeparting from the scope and spirit of the invention. Those skilled inthe art could implement various other feature combinations withoutdeparting from the scope and spirit of the invention.

The invention claimed is:
 1. A method for calibrating a time delayestimation circuit comprising: generating a calibration pulse;determining a filter response of the calibration pulse with a firstfilter array; determining a filter response of the calibration pulsewith a second filter array; determining, by a processor, based at leaston the filter response of the calibration pulse determined with thefirst filter array and the filter response of the calibration pulsedetermined with the second filter array, a phase correction; amplifyingthe calibration pulse; determining a filter response of the amplifiedcalibration pulse with a third filter array; and selecting either thefilter response of the calibration signal or the filter response of theamplified calibration signal as the filter response of the calibrationpulse determined with the second filter array for determining the phasecorrection.
 2. The method of claim 1 further comprising: sampling thefilter response of the calibration pulse determined with the firstfilter array; sampling the filter response of the calibration pulsedetermined with the second filter array; and wherein the phasecorrection is determined based at least on the sampled filter responseof the calibration pulse determined with the first filter array and thesampled filter response of the calibration pulse determined with thesecond filter array.
 3. An apparatus for calibrating a time delayestimation circuit comprising: a calibration pulse generator; a firstfilter array adapted to determine a filter response of a calibrationpulse; a second filter array adapted to determine a filter response ofthe calibration pulse; a processor adapted to determine, based at leaston the filter response of the calibration pulse determined with thefirst filter array and the filter response of the calibration pulsedetermined with the second filter array, a phase correction; anamplifier adapted to amplify the calibration pulse; a third filter arrayadapted to determine a filter response of the amplified calibrationpulse; and a switch adapted to select either the filter response of thecalibration signal or the filter response of the amplified calibrationsignal as the filter response of the calibration pulse determined withthe second filter array for determining the phase correction.
 4. Theapparatus of claim 3 further comprising: a first sampler adapted tosample the filter response of the calibration pulse determined with thefirst filter array; a second sampler adapted to sample sampling thefilter response of the calibration pulse determined with the secondfilter array; and wherein the processor is further adapted to determinethe phase correction based at least on the sampled filter response ofthe calibration pulse determined with the first filter array and thesampled filter response of the calibration pulse determined with thesecond filter array.